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An alternative name for an associated Legendre polynomial.

The zeros of the derivative P^'(z) of a polynomial P(z) that are not multiple zeros of P(z) are the positions of equilibrium in the field of force due to unit particles ...

An approach for the calculation of a Gröbner basis into several smaller computations following a path in the Gröbner fan of the ideal generated by the system of inequalities.

The branch of algebraic topology which deals with homotopy groups. Homotopy methods can be used to solve systems of polynomials by embedding the polynomials in a family of ...

Q_n^((alpha,beta))(x)=2^(-n-1)(x-1)^(-alpha)(x+1)^(-beta) ×int_(-1)^1(1-t)^(n+alpha)(1+t)^(n+beta)(x-t)^(-n-1)dt. In the exceptional case n=0, alpha+beta+1=0, a nonconstant ...

A Jensen disk is a disk in the complex plane whose diameter joins complex conjugate roots of a polynomial (Trott 2004, p. 22).

An algebraically soluble equation of odd prime degree which is irreducible in the natural field possesses either 1. Only a single real root, or 2. All real roots.

A quantity involving primitive cube roots of unity which can be used to solve the cubic equation.

For an arbitrary not identically constant polynomial, the zeros of its derivatives lie in the smallest convex polygon containing the zeros of the original polynomial.

A k-matching in a graph G is a set of k edges, no two of which have a vertex in common (i.e., an independent edge set of size k). Let Phi_k be the number of k-matchings in ...